I do not restart my server manually and do not have any stuff like this at a set timer but randomly when open rust admin to check my server (for last week 4 times at least) saw that RCON tool says Offline. I am on Linux and open my Putty to see the server, it's OFFLINE. I do start it but what? Why? When? I have a lot of questions here that can't find the answer myself. I am not good at linux and also not sure where the logs are stored. I need to somehow enable hard logs and see the f*cking reason for server shutdown. If vps somehow loose connection should be back online after that but nope connection is fine, just server process looks like terminated or just stopped. 

Thanks in advance and hope someone can help.

What are you using to manage your server? If it has a monitor feature you should run that every 10 mins or so in a crontab entry to restart your game server in the event of a crash.

If you aren't using anything to manage your server, then you should look at LinuxGSM.

I have Linux GSM and not sure how to actually work with it at full power potential...
I used to do start/stop and update/mu to do updates when needed and start the server then all my main work is via RustAdmin... Somehow found logs of LinxGSM but nothing again inside... Host told me that might be because of low ram but I am with 10GB so sounds fine... Anyways server stopped to do these weird random stops but how I can auto start it in case of the same problems again?

You can set up a cron job to run:

~/rustserver m​

free​

ok thanks for reply, I will do check this out.
Also still not sure if that was caused the stops because support of the host told me this as possible scenario this with the low ram. I am happy last week had no problem with this so I hope its ok.